Nowaczyk, Nikolai (2013) Continuity of Dirac spectra. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 44 (4). pp. 541-563. ISSN 0232-704X, 1572-9060
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It is well known that on a bounded spectral interval the Dirac spectrum can be described locally by a non-decreasing sequence of continuous functions of the Riemannian metric. In the present article, we extend this result to a global version. We view the spectrum of a Dirac operator as a function and endow the space of all spectra with an -uniform metric. We prove that the spectrum of the Dirac operator depends continuously on the Riemannian metric. As a corollary, we obtain the existence of a non-decreasing family of functions on the space of all Riemannian metrics, which represents the entire Dirac spectrum at any metric. We also show that, due to spectral flow, these functions do not descend to the space of Riemannian metrics modulo spin diffeomorphisms in general.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HARMONIC SPINORS; OPERATORS; METRICS; FLOW; Spin Geometry; Dirac Operator; Spectral Geometry; Dirac Spectrum; Spectral Flow |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 Mar 2020 06:44 |
| Last Modified: | 25 Mar 2020 06:44 |
| URI: | https://pred.uni-regensburg.de/id/eprint/15613 |
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